A large body of research has focused on efficient and scalable processing of subgraph search queries on large networks. In these efforts, a query is posed in the form of a connected query graph. Unfortunately, in practice end users may not always have precise knowledge about the topological relationships between nodes in a query graph to formulate a connected query. In this paper, we present a novel graph querying paradigm called partial topology-based network search and propose a query processing framework called panda to efficiently process partial topology query (ptq) in a single machine. A ptq is a disconnected query graph containing multiple connected query components. ptqs allow an end user to formulate queries without demanding precise information about the complete topology of a query graph. To this end, we propose an exact and an approximate algorithm called sen-panda and po-panda, respectively, to generate top-k matches of a ptq. We also present a subgraph simulation-based optimization technique to further speedup the processing of ptqs. Using real-life networks with millions of nodes, we experimentally verify that our proposed algorithms are superior to several baseline techniques.